mean and Standard deviation of ratio of normal variables?

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Deepak Kumar
Deepak Kumar 2019-4-12
编辑： Image Analyst 2019-4-14
If we have, Z=X / Y,
where X and Y have different means and normally distributed, then
what is the mean and standard deviation of Z?
We know that is a Cauchy Distribution, so Z may be approximately normally distributed. Here is the Journal article discussing the ratio of normal variables:
link to journal article.
My question is, can we find exact distribution of Z ?

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回答（1 个）

Bjorn Gustavsson
Bjorn Gustavsson 2019-4-14
Well, you have the document to read. If that's not good enough there is always:
Ratio-distributions (wikipedia),
Distribution-function of ratio of 2 normal random variables (AIP),
On the ratio of two correlated normal random variables (Biometrica)
Hopefully you find what you're looking for there.

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